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The bigger the prime numbers used, the more possible combinations there are to create the public key and the harder it is to find the right combination. In reality, there is more computation involved.
Any number is the unique product of prime factors. Eratosthenes, who lived from -276 to -194, proposed a process that allows us to find all prime numbers less than a given natural number N.
Today, people use complex computing networks to search for prime numbers with millions of digits. But early mathematicians were running these calculations by hand.